Communicating the sum of sources over a network

We consider a network (that is capable of network coding) with a set of sources and terminals, where each terminal is interested in recovering the sum of the sources. Considering directed acyclic graphs with unit capacity edges and independent, unit-entropy sources, we show the rate region when (a) there are two sources and n terminals, and (b) n sources and two terminals. In these cases as long as there exists at least one path from each source to each terminal we demonstrate that there exists a valid assignment of coding vectors to the edges such that the terminals can recover the sum of the sources.

我们考虑使用一组来源和终端的网络（能够进行网络编码），每个终端都对恢复来源的总和感兴趣。考虑到具有单位容量边缘和独立的单位entropy源的定向无环图，我们显示了（a）有两个源和n端子时的速率区域，以及（b）N来源和两个端子。在这些情况下，只要每个源到每个终端的至少有一个路径，我们就证明存在对向量编码向量的有效分配，以便终端可以恢复源的总和。